Results 1 to 3 of 3

Math Help - General solution of a differential equation

  1. #1
    Member
    Joined
    Dec 2008
    Posts
    105

    General solution of a differential equation

    Hi,

    I have to solve the general equation for this differential

    \frac{d^2y}{dx^2} - 6\frac{dy}{dx} + 9y = 50\sin(x)

    I have the homogeneous equation as (A + Bx)e^{3x}

    However now that I am trying to get the partial equation I am stuck, I am unsure as what to use for the y_{PI} = k(something) I have tried using sin(x) but that gets difficult to untangle

    Thanks

    Beard
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,992
    Thanks
    1129
    You will need both sine and cosine:

    y= A cos(x)+ B sin(x)

    y'= -Asin(x)+ Bcos(x)

    y"= -Acos(x)- Bsin(x)

    y"- 6y+ 9y= -Acos(x)- Bsin(x)- 6Asin(x)+ 6Bcos(x)+ 9Acox(x)+ 9Bsin(x)

    = (-A+ 6B+ 9A) cos(x)+ (-B- 6A+ 9B) sin(x)

    = (8A+ 6B) cos(x) + (8B- 6A) sin(x)= 50 sin(x)

    Solve 8A+ 6B= 0, 8B- 6A= 0 for A and B.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Dec 2008
    Posts
    105
    Quote Originally Posted by HallsofIvy View Post
    You will need both sine and cosine:

    y= A cos(x)+ B sin(x)

    y'= -Asin(x)+ Bcos(x)

    y"= -Acos(x)- Bsin(x)

    y"- 6y+ 9y= -Acos(x)- Bsin(x)- 6Asin(x)+ 6Bcos(x)+ 9Acox(x)+ 9Bsin(x)

    = (-A+ 6B+ 9A) cos(x)+ (-B- 6A+ 9B) sin(x)

    = (8A+ 6B) cos(x) + (8B- 6A) sin(x)= 50 sin(x)

    Solve 8A+ 6B= 0, 8B- 6A= 0 for A and B.
    I wasn't actually expecting all of that, I was just asking for the first bit y= A cos(x)+ B sin(x) but thanks anyway.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. general solution of this differential equation?
    Posted in the Differential Equations Forum
    Replies: 5
    Last Post: September 10th 2010, 07:57 AM
  2. General Solution of a Differential Equation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: March 17th 2010, 02:39 AM
  3. general solution of a differential equation
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: December 5th 2009, 07:30 AM
  4. General solution to differential equation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: November 13th 2009, 03:32 PM
  5. General Solution of Differential Equation
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: November 17th 2008, 04:46 PM

Search Tags


/mathhelpforum @mathhelpforum